Optical properties of superconducting pressurized LaH10

Recently superconductivity has been discovered at around 200 K in a hydrogen sulfide system and around 260 K in a lanthanum hydride system, both under pressures of about 200 GPa. These record-breaking transition temperatures bring within reach the long-term goal of obtaining room-temperature superconductivity. We have used first-principles calculations based on density functional theory along with Migdal-Eliashberg theory to investigate the electron-phonon mechanism for superconductivity in the $Fm\overline{3}m$ phase proposed for the ${\mathrm{LaH}}₁₀$ superconductor. We show that the very high transition temperature ${T}_c$ results from a highly optimized electron-phonon interaction that favors coupling to high-frequency hydrogen phonons. Various superconducting properties are calculated, such as the energy gap, the isotope effect, the specific heat jump at ${T}_c$, the thermodynamic critical field, and the temperature-dependent penetration depth. However, our main emphasis is on the finite-frequency optical properties, measurement of which may allow for an independent determination of ${T}_c$ and also a confirmation of the mechanism for superconductivity.